Look, we’re all pretty sure 3-SAT can’t be solved in polynomial time. So when this comes up—as happens multiple times a day—we all know where to turn. Say it with me: the Exponential Time Hypothesis (ETH). I mean, sure, that’s unproven too, but it gives us all a good idea of how much non-polynomial time something is going to take.
Or does it??? Because OpenAI claims to have just disproved the entire ETH. Back to the drawing board everyone!
I’m actually just paraphrasing a YouTube video about the ETH (probably badly) and have zero idea what I’m talking about. But if you’re a theoretical computer scientist working with optimization and algorithms, this matters. And OpenAI is claiming this and two other breakthroughs in its latest science dump.
In addition to believing its AI models have disproved the ETH, OpenAI claims to have resolved something from the study of waves and harmonics called “the Kakeya conjecture” by finding a novel proof for all dimensions in something called “the local smoothing conjecture.”
But don’t get too relaxed thinking about all those smooth waves, because over in physics, OpenAI also thinks it has a proof of “certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.” Yep, you read that right: gauge fields and fermions!
When OpenAI dumped 377 math results on GitHub at the beginning of this month, its blog post included parts that came across as a bit defensive, including language about how OpenAI would “empower scientists with state-of-the-art capabilities,” and work to “responsibly release the model that produced these results.“ An advisory group it had worked with had already spoken out against a private company using unreleased internal AI models to achieve breakthrough results, and OpenAI had apparently done that.
This time, OpenAI assures the reader that OpenAI does not “seek academic credit for the discoveries produced by our internal models.” And apparently to that end, it has a plan that it hopes will disperse AI-generated discoveries—and therefore credit—to the math and physics communities. But it’s a plan that, taken to extremes, could be reminiscent of Immortan Joe in the movie Mad Max: Fury Road, dispersing water to his parched subjects.
OpenAI is releasing model-generated texts, and says they’re “best understood as a form of raw research data,” and that the task of the math and science communities will be to “convert this raw research data into scientific understanding.”
The math results, OpenAI says, were “formalized” or “verified” in Lean, a proof assistant tool meant to reduce the need to check and recheck work. Lean reliance has already been an issue for OpenAI, since human readers digging around in OpenAI’s Lean-verified solution—supposedly—to the Navier-Stokes Millenium Problem became concerned that Lean verified a weaker assertion than what was initially written in what OpenAI published.
Amid these growing pains, OpenAI says it has already “reached out to external experts”—often the very scholars upon whose work the models are building—and says it wants them to act as “shepherds,” who will put together groups who will then convert these AI outputs into, well, new human knowledge. Though in the blog post, OpenAI acknowledges that “choosing initial shepherds necessarily shapes who gets involved first and creates asymmetry of information.”
For what it’s worth, some of the “raw” information is now on GitHub—but not all of it. The group working on physics, for instance, has decided, OpenAI says, “to hold off on releasing the AI-produced artifacts and instead work on writing it up themselves.”
